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An implementation of "MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing" (ICML 2019).
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| 2026-08-06 | 406 |
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MixHop and N-GCN
===========================
[](https://paperswithcode.com/sota/node-classification-on-citeseer?p=mixhop-higher-order-graph-convolution)
[](https://arxiv.org/abs/1905.00067)
[](https://codebeat.co/projects/github-com-benedekrozemberczki-mixhop-and-n-gcn-master)
[](https://github.com/benedekrozemberczki/MixHop-and-N-GCN/archive/master.zip)⠀[](https://twitter.com/intent/follow?screen_name=benrozemberczki)
A **PyTorch** implementation of "MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing" (ICML 2019) and "A Higher-Order Graph Convolutional Layer" (NeurIPS 2018).
<p align="center">
<img width="800" src="mixhop1.jpg">
</p>
---------------------
### Abstract
<p align="justify">
Recent methods generalize convolutional layers from Euclidean domains to graph-structured data by approximating the eigenbasis of the graph Laplacian. The computationally-efficient and broadly-used Graph ConvNet of Kipf & Welling, over-simplifies the approximation, effectively rendering graph convolution as a neighborhood-averaging operator. This simplification restricts the model from learning delta operators, the very premise of the graph Laplacian. In this work, we propose a new Graph Convolutional layer which mixes multiple powers of the adjacency matrix, allowing it to learn delta operators. Our layer exhibits the same memory footprint and computational complexity as a GCN. We illustrate the strength of our proposed layer on both synthetic graph datasets, and on several real-world citation graphs, setting the record state-of-the-art on Pubmed.</p>
This repository provides a PyTorch implementation of MixHop and N-GCN as described in the papers:
> MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing
> Sami Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Hrayr Harutyunyan, Nazanin Alipourfard, Kristina Lerman, Greg Ver Steeg, and Aram Galstyan.
> ICML, 2019.
> [[Paper]](https://arxiv.org/pdf/1905.00067.pdf)
> A Higher-Order Graph Convolutional Layer.
> Sami A Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Nazanin Alipourfard, Hrayr Harutyunyan.
> NeurIPS, 2018.
> [[Paper]](http://sami.haija.org/papers/high-order-gc-layer.pdf)
The original TensorFlow implementation of MixHop is available [[Here]](https://github.com/samihaija/mixhop).
### Requirements
The codebase is implemented in Python 3.5.2. package versions used for development are just below.
```
networkx 2.4
tqdm 4.28.1
numpy 1.15.4
pandas 0.23.4
texttable 1.5.0
scipy 1.1.0
argparse 1.1.0
torch 1.1.0
torch-sparse 0.3.0
```
### Datasets
<p align="justify">
The code takes the **edge list** of the graph in a csv file. Every row indicates an edge between two nodes separated by a comma. The first row is a header. Nodes should be indexed starting with 0. A sample graph for `Cora` is included in the `input/` directory. In addition to the edgelist there is a JSON file with the sparse features and a csv with the target variable.</p>
<p align="justify">
The **feature matrix** is a sparse binary one it is stored as a json. Nodes are keys of the json and feature indices are the values. For each node feature column ids are stored as elements of a list. The feature matrix is structured as:</p>
```javascript
{ 0: [0, 1, 38, 1968, 2000, 52727],
1: [10000, 20, 3],
2: [],
...
n: [2018, 10000]}
```
<p align="justify">
The **target Excerpt of 6,740 characters
Read on GitHubWould you bet a product on this? Bounded 0–100 and slow moving.
matched fp:c7f7c5979343b93b, topic:deep-learning, topic:pytorch, topic:tensorflow